Problem: Simplify the following expression: $\dfrac{90z^3}{70z^3}$ You can assume $z \neq 0$.
Answer: $ \dfrac{90z^3}{70z^3} = \dfrac{90}{70} \cdot \dfrac{z^3}{z^3} $ To simplify $\frac{90}{70}$ , find the greatest common factor (GCD) of $90$ and $70$ $90 = 2 \cdot 3 \cdot 3 \cdot 5$ $70 = 2 \cdot 5 \cdot 7$ $ \mbox{GCD}(90, 70) = 2 \cdot 5 = 10 $ $ \dfrac{90}{70} \cdot \dfrac{z^3}{z^3} = \dfrac{10 \cdot 9}{10 \cdot 7} \cdot \dfrac{z^3}{z^3} $ $\phantom{ \dfrac{90}{70} \cdot \dfrac{3}{3}} = \dfrac{9}{7} \cdot \dfrac{z^3}{z^3} $ $ \dfrac{z^3}{z^3} = \dfrac{z \cdot z \cdot z}{z \cdot z \cdot z} = 1 $ $ \dfrac{9}{7} \cdot 1 = \dfrac{9}{7} $